Four-membered rings are rapidly becoming sought-after scaffolds in pharmaceuticals due to their rigid structure and well-defined exit vectors. Towards this goal, we developed a method to enantioselectively form cyclobutenes from simple olefins and N-sulfonyl-1,2,3-triazoles. While these triazoles are known to act as diazo precursors via ring-chain tautomerization, we recognized them as vicinal dicarbene equivalents. Thus, alkynes are reacted in [3+2] cycloadditions with azides to form triazoles, which are then reacted with alkenes in a formal [2+2] cycloaddition. A host of enantioenriched cyclobutenes were synthesized, several of which were carried on to assemble the carbon skeletons of several natural products. The ability to selectively delete, insert, or exchange atoms in the core scaffolds of molecules is of fundamental interest to synthetic chemists and could be of great use to medicinal chemists seeking to rapidly modulate the parameters of lead compounds. Though atom deletions and insertions have garnered much interest in the form of ring contractions and expansions, atom exchanges have seen considerably less development. One notable exchange that has eluded chemists is the conversion of benzene to pyridine, which is of interest due to the "necessary nitrogen atom" effect, which describes the enhancement of key pharmacological properties when an arene in a lead compound was replaced with a pyridine. To this end, we found that azides serve as effective nitrene precursors to engage arenes in a C to N atom exchange sequence featuring nitrogen atom insertion and carbon atom deletion

This thesis presents the experimental studies of quantum-controlled cold scattering of H2 isotopologues (HD, D2) with simple rare gas atoms (He, Ne) and diatom molecules D2. In these experiments, we prepare HD and D2 molecules in specific rovibrational levels (v = 2, 4, j = 2, 4) with defined alignments, and study their rotational inelastic scatterings of the state-prepared molecules at low collision temperatures. From a time-of-flight apparatus, we extract information about the angular distributions of the scattered products, therefore providing insights into the dynamics of the collision processes. By combining quantum-state control and low-energy scattering, we are able to interrogate the fundamental interactions between such simple atoms and diatoms at an unprecedented level of detail. The thesis is structured as follows. Chapter 1 serves as an introductory point of the subject. A brief overview of the development and progress of cold scattering is given, and various techniques to achieve cold relative temperatures as well as quantum state control are discussed. The purpose is mainly to situate our experimental techniques in the broad field, and to demonstrate the similarities and difficulties we face. Chapter 2 presents the theoretical treatment of the scattering problem. They serve as the necessary background for analyzing the data in later discussions, and sometimes provide direct comparisons. Chapter 3 focuses on the experimental setup we use to achieve quantum-controlled cold scattering. Many details are elucidated at length. In the next two chapters (Chapter 4, 5), various experimental results of rovibrationally excited HD/D2 with other scattering partners are presented and discussed. Chapter 4 describes the Δj = 2 inelastic scattering results of D2 (v = 2, 4, j = 2, 4) with rare gas atoms He and Ne, as well as the Δj = 1, 2 relaxations of HD (v = 4, j = 2). Chapter 5 includes the scattering results between a pair of state-prepared diatoms D2 (v = 2, j = 2). In these two chapters, theoretical comparisons are provided alongside the data where available. In the last chapter (Chapter 6), we conclude the thesis with more thoughts on the summary and outlook of the project. Although complete satisfactory agreements between theory and experiments have not been necessarily achieved for all of the studies we present, we hope such discussions would inspire more future works of this kind

Robust and efficient 3D scene understanding could enable embodied agents to safely interact with the physical world in real-time. The key to the remarkable success of computer vision in the last decade owes to the rediscovery of convolutional neural networks. However, this technology does not always directly translate to 3D due to the curse of dimensionality. The size of the data grows cubically with the voxels, and the same level of input resolution and network depth was infeasible compared to that of 2D. Based on the observation that the 3D space is mostly empty, sparse tensors and sparse convolutions stand out as an efficient and effective 3D counterparts to the 2D convolution by exclusively operating on non-empty spaces. Such efficiency gain supports deeper neural networks for higher accuracy in real-time reference speed. To this end, this thesis explores the application of sparse convolution to various 3D scene understanding tasks. This thesis breaks down a holistic 3D scene understanding pipeline into the following subgoals; 1. data collection from 3D reconstruction, 2. semantic segmentation, 3. object detection, and 4. multi-object tracking. With robotics applications in mind, this thesis aims to achieve better performance, scalability, and efficiency in understanding the high-level semantics of the spatio-temporal domain while addressing the unique challenges the sparse data poses. In this thesis, we propose generalized sparse convolution and demonstrate how our method 1. gains efficiency by leveraging the sparseness of the 3D point cloud, 2. achieves robust performance by utilizing the gained efficiency, 3. makes predictions on empty spaces by dynamically generating points, and 4. jointly solves detection and tracking with spatio-temporal reasoning. Altogether, this thesis proposes an efficient and reliable pipeline for a holistic 3D scene understanding

To meet the exploding information processing and data storage demands, memory technology, as one of the cornerstones in modern computing systems, faces the constant challenge of advancing to the next technology node with a larger capacity and higher density. As difficulties arise in the further scaling of conventional memories, new memories show the potentials to bridge the performance gap between memory and storage, providing new opportunities to innovate computing systems and architectures. Among emerging memories, resistive switching memory (RSM) is a promising solution due to its high device density and reasonably fast write/read operation speed. Resistive random-access memory (RRAM), as an example of RSM, has a simple structure and uses low-temperature fabrication that is compatible with back-end-of-the-line (BEOL) metal wiring of typical CMOS logic technology, thus potentially leading to low cost and on-chip integration with logic for high bandwidth access. Research efforts have been made to explore various material options, device and array structures, and chip architectures. However, to achieve an ultrahigh-density memory, a practical co-design must take into account all the above considerations to arrive at a superior solution. In this dissertation, I present a way to realize ultrahigh-density memory with 3D vertical RRAM (VRRAM). I develop a design guideline for ultrahigh-density 3D VRSM using simulations of 3D memory arrays based on an accurate and computationally efficient model of the memory and parasitic resistance of the memory wired in 3D. I detail the model formulation and validation with physics-based simulations. Combined with simulation results, I discuss design specifications for different physical levels from device to array to chip architecture and provide a comprehensive list of design tasks to achieve an ultrahigh-density 3D VRRAM. To prioritize design tasks among different levels, I focus on the rudimentary design constraints at the device level and extend design requirements to a ready-to-build memory device in the lab. I then experimentally demonstrate an 8-layer 3D Ru/AlOxNy/TiN VRRAM towards an ultrahigh-density memory. This 3D VRRAM satisfies the design requirements for a tera-bit class memory when integrated with a proper selector. I further investigate the downscaling potentials of 3D VRRAM based on experimental data and ongoing scaling techniques and trends in the industry. Incorporating these scaling prospects, I project that 3D VRRAM can achieve a much higher density and capacity with the same number of 3D layers and fewer bits per cell compared to the state-of-the-art 3D NAND. With the structural and process flexibility (e.g., BEOL), 3D VRRAM can expand its high-density applications to be integrated on-chip with CMOS logic for high bandwidth memory access

Optimizing the design and performance of photonic systems has been an active and growing area of research over the past decade with many practical applications such as image sensors, augmented reality and virtual reality, on-chip photonic systems, and more. Moreover, gradient-based methods, such as the adjoint variable method (AVM), have led to very distinctive and complex designs for on-chip multiplexers, tapers, dielectric laser accelerators, and more, while yielding much higher performance metrics which classical design approaches using first principles physics cannot match. However, less research has been dedicated in the photonics community to understanding and improving the underlying numerical methods which are critical for the success of these applications. In this thesis, we will demonstrate four key numerical advancements in the use of gradient-based design methods using frequency domain numerical solvers of Maxwell's equations, particularly finite difference frequency domain (FDFD) solvers. The first is the application of domain decomposition techniques to gradient-based optimization, allowing us to reduce the effective system size for a gain in efficiency. The second exploits the physics of perturbative series expansions to efficiently determine the optimal learning rate essential to gradient-based optimization. The third leverages the fundamental similarities of the previous two methods, allowing us to combine the two to achieve a further multiplicative acceleration. The fourth is exploiting the choice of boundary condition in the context of perfectly matched layers to minimize overhead and optimize the efficiency of the simulations required during the optimization procedure. Furthermore, we will demonstrate one novel practical application in designing a next generation replacement for traditional filter-based image sensors that we term a 'color router'. By using a gradient-based approach, we demonstrate not only can we overcome the traditional limitations of filter-based approaches, but we can approach the absolute physical limit of color separation efficiency. In the context of this problem as well, we also demonstrate one further novel method to accelerate optimization, using an L1-like penalty method inspired by L1-regularization popularized in machine learning to improve the robustness to manufacturing errors and other perturbations to the device design. Finally, as a contrast to the gradient-based technique of optimization, we also showcase two examples of more traditional device optimization using the theoretical principles of Maxwell's equations. The first is to exploit analytic continuation and the band-structure of insulator-metal-insulator waveguides to design a reflector with superior reflection properties to that of a uniform metal but with lower loss (essentially a nearly metal-less metallic metamaterial). The second is to engineer interesting radiative properties and extraordinarily high reflection in atomically-thin monolayer graphene nano-ribbon system